From there you need to learn server side code - PHP would probably be the easiest to pick up and run with, but Python, ASP, Perl, Ruby... whatever server side language you have access to and are willing to learn... are the next step.
That's a different discussion, and also a discussion about integration of libraries based on need.
Responsive for the noob - you can use a front-end framework like Bootstrap - but there are others. However, making it look DIY is a lot of work. You can get simple drop-in css snippets that will make your site responsive without the need to crank up the whole shebang of a framework. As mentioned, if you're serious about web dev, you need to learn the nuts and bolts, not just lever a bit of putty to fill a hole.
Dropping in third party scripts is a recipe for disaster unless you can work out what they're doing - I'm thinking security and performance.
By downloading and implementing Bootstrap you will not learn how to create responsive websites. It's a shortcut and you can create them, but without knowing the core concept of RWD (media queries, fluid grids and flexible media) you will allways be dependend on a framework like Bootstrap and its features, snippets and templates. If you want to create custom & lightweight responsive websites optimized for whatever screen or device it will be viewed on, you will have to get your hands dirty.